Analysis in a Formal Predicative Set Theory

Nissan Levi*, Arnon Avron

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We present correct and natural development of fundamental analysis in a predicative set theory we call PZFU. This is done by using a delicate and careful choice of those Dedekind cuts that are adopted as real numbers. PZFU is based on ancestral logic rather than on first-order logic. Its key feature is that it is definitional in the sense that every object which is shown in it to exist is defined by some closed term of the theory. This allows for a very concrete, computationally-oriented model of it, and makes it very suitable for MKM (Mathematical Knowledge Management) and ITP (Interactive Theorem Proving). The development of analysis in PZFU does not involve coding, and the definitions it provides for the basic notions (like continuity) are the natural ones, almost the same as one can find in any standard analysis book.

Original languageEnglish
Title of host publicationLogic, Language, Information, and Computation - 27th International Workshop, WoLLIC 2021, Proceedings
EditorsAlexandra Silva, Renata Wassermann, Ruy de Queiroz
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages17
ISBN (Print)9783030888527
StatePublished - 2021
Event27th International Workshop on Logic, Language, Information and Computation, WoLLIC 2021 - Virtual, Online
Duration: 5 Oct 20218 Oct 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13038 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference27th International Workshop on Logic, Language, Information and Computation, WoLLIC 2021
CityVirtual, Online


  • Computable set theories
  • Foundation of mathematics
  • Predicativity


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